Preheat the oven to 350 degrees. Slice the jalapeños lengthwise. Use a spoon to scoop out the seeds and white pith. Place the jalapeño halves, cut side up, on a baking sheet. 

Bring a medium pot of salted water to a boil. Meanwhile, peel the potato and cut it into 1-inch cubes. When the water is boiling, carefully add the potatoes. Cook for 20 to 25 minutes, until the potatoes are soft. Drain them in a colander.

Place the warm potatoes in a large bowl along with the milk, sour cream, butter, salt, and pepper. Use a fork to mash everything together. Stir in the bacon and chives. Use a spoon to divide the mashed potatoes among the jalapeño slices, mounding the potatoes inside the jalapeño shells. Sprinkle with the cheddar cheese, and bake for 25 to 30 minutes, until the jalapeños are soft and the cheese is browned and melty.